报告人: 马东魁（华南理工大学）

日  期: 2019年11月2日

时  间: 上午10:30

地  点: 理科楼 LA106

摘  要: In this paper we introduce the topological entropy and lower and upper capacity topological entropies of a free semigroup action, which extends the notion of the topological entropy of a free semigroup action defined by Bufetov, by using the Carath ́eodory-Pesin structure (C-P structure). We provide some properties of these notions and give three main results. The first is the relationship between the upper capacity topological entropy of a skew- product transformation and the upper capacity topological entropy of a free semigroup action with respect to arbitrary subset. The second are a lower and a upper estimations of the topological entropy of a free semigroup action by local entropies. The third is that for any free semigroup action with m generators of Lipschitz maps, topological entropy for any subset is upper bounded by the Hausdorff dimension of the subset multiplied by the maximum logarithm of the Lipschitz constants. The results of this paper generalize results of Bufetov, Ma et al., and Misiurewicz.

报告人简介：马东魁，华南理工大学数学学院教授。研究方向为动力系统与遍历理论。主持完成多项国家自然科学基金，在Ergodic Theory Dynam. Systems、 Discrete & Continuous Dynamical Systems- A等期刊上发表高水平SCI论文40余篇。

公司联系人:孔德荣

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